The Hochschild-Kostant-Rosenberg isomorphism for quantized analytic cycles

Details The Hochschild-Kostant-Rosenberg isomorphism for quantized analytic cycles The Hochschild-Kostant-Rosenberg isomorphism for quantized analytic cycles

2011-09-04

arxiv.org/abs/1109.0739v2

Mathematics

Algebraic Geometry

Mistake corrected in Section 5.2

Scientific paper

In this article, we provide a detailed account of a construction sketched by Kashiwara in an unpublished manuscript concerning generalized HKR isomorphisms for smooth analytic cycles whose conormal exact sequence splits. It enables us, among other applications, to solve a problem raised recently by Arinkin and C\u{a}ld\u{a}raru about uniqueness of such HKR isomorphisms in the case of the diagonal injection. Using this construction, we also associate with any smooth analytic cycle endowed with an infinitesimal retraction a cycle class which is an obstruction for the cycle to be the vanishing locus of a transverse section of a holomorphic vector bundle.

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